The 2-D DNSs of the ignition of a lean PRF/air mixture under RCCI/SCCI conditions were performed by varyingrandu0 at differentT0 with negatively-correlatedT–rfields. It was found that in the low- and intermediate-temperature regimes, the RCCI combustion is more apt to occur earlier than the corresponding SCCI combustion; its mean HRR is more distributed over time. This is primarily attributed to the high sensitivity of the ignition of the PRF/air mixture to PRF0 within the negative temperature coefficient (NTC) regime. In the high-temperature regime, however, the difference between RCCI and SCCI combustion becomes marginal because the ignition of the PRF/air mixture is highly-sensitive to T0 rather than PRF0 and φ0. The Damk¨ohler number analysis verifies that the temporal spread of the mean HRR by fuel stratification is due to the increase of deflagration mode of combustion. Finally, it is found that turbulence is more likely to homogenize the initial mixture of both RCCI and SCCI cases, and as such, the overall combustion occurs more by spontaneous ignition mode with increasing u0. These results suggest that an HCCI-type combustion can be controlled by properly adjusting T0, φ0, and PRF0, depending onT0 relative to the NTC regime.
Chapter III
The ignition characteristics of PRF/air mixtures under
RCCI/SCCI conditions: Chemical
aspects
In this Chapter III, chemical aspects of a lean PRF/air mixture under RCCI/SCCI conditions are investigated by analyzing DNS data in the previous Chapter II with chem- ical explosive mode analysis (CEMA).
3.1 Methodology
To investigate the chemical aspects of RCCI and SCCI combustion, we analyze 2-D DNS data set in [51] using CEMA. The 2-D DNSs of the ignition of the PRF/air mixture under RCCI and SCCI conditions were simulated using the Sandia compressible DNS code [52], S3D, with a 116-species reduced chemistry of PRF oxidation [44]. Note that recent theoretical and experimental findings on hydroperoxyalkyl (QOOH) chemistry [53–56]
have not been updated in the present PRF reduced mechanism. However, it still shows good agreement with experimental results in terms of ignition delays, flame propagation speeds, and extinction residence times [44].
The initial conditions for DNSs are specified as follows. The initial pressure, p0, mean equivalence ratio, φ0, are 40 atm and 0.45, respectively. PRF50 (i.e., a 50% iso- octane and 50% n-heptane blend by volume) was adopted as the mean fuel for RCCI combustion and the single fuel for SCCI combustion. For RCCI cases, n-heptane field is initialized by m = m + m0, superimposed on a uniform iso-octane/air mixture, where m is the mass of n-heptane, and the ‘overbar’ and0 represent the mean and fluctuation, respectively. For SCCI cases, PRF50 is supplied through two-stage injection and hence,m represents the mass of PRF50. The local variations in PRF number, equivalence ratio, and temperature can be achieved for RCCI combustion, while only variations in equivalence ratio and temperature are obtained for SCCI combustion. The initial turbulent flow field is generated using an isotropic kinetic energy spectrum function by Passot-Pouquet [46].
Concentration and temperature fields are also generated from the same energy spectrum as turbulence with different random number and then are superimposed on top of the turbulence field. The periodic boundary conditions are imposed in all directions, and as such, RCCI/SCCI combustion occurs in constant volume. For more details of the numerical setup, readers are referred to [51].
Two representative RCCI/SCCI cases (i.e., Case 6 for RCCI and Case 8 for SCCI in [51]) with the degree of fuel stratification, r = m0/m = 0.44, temperature fluctu- ation, T0 = 30 K, at the initial mean temperature, T0 = 900 K, are chosen for the present CEMA such that both cases are initially involved in the low- and intermediate- temperature chemistries. The 0-D homogeneous ignition delay, τig0, of PRF50 is 2.2 ms.
For both cases, negatively-correlated T–r field is assumed to consider the evaporative cooling effect of directly-injected fuel.
Note that CEMA has been applied to various DNS studies [42, 57–62] to elucidate the chemical aspects of turbulent combustion and is now believed as one of the useful computational flame diagnostics tools for the systematic detection of important species and reactions in premixed flames and flame ignition/extinction. Also note that the char- acteristics of two-stage ignition of large hydrocarbon fuel/air mixtures have been numer- ically investigated by adopting the computational singular perturbation method [63] and CEMA [6, 38, 44, 45, 62, 64, 65].
CEMA is briefly explained here. For more details of CEMA, readers are referred to [58, 59, 62]. For a chemically-reacting system, the discretized conservation equations can be expressed as:
Dy
Dt =g(y) = ω(y) +s(y), (3.1) whereD/Dt is the material derivative, which can be replaced by d/dt in the Lagrangian coordinate. y denotes the solution variables including species concentrations and tem- perature. ω and s represent respectively the chemical source term and all the other non-chemical source terms such as diffusion in flames and homogeneous mixing term in stirred reactors.
Since the Jacobian of the chemical source term, Jω (≡∂ω/∂y), retains the chemical information of local mixture, the chemical feature of the mixture can be determined based on the Jacobian. To capture the chemical feature in CEMA, a chemical mode is defined as an eigenmode of Jω, which is associated with an eigenvalue, λe, and a corresponding pair of the left and right eigenvectors, ae and be. Chemical explosive mode (CEM) is a chemical mode of which real part of eigenvalue is positive, Re(λe)> 0.
In general, a local mixture with a CEM is destined to auto-ignite if there are no thermal and radical losses. Therefore, CEM indicates an intrinsic chemical feature of ignitable mixture: i.e., a mixture with Re(λe) > 0 is more apt to ignite while a mixture with Re(λe) < 0 is already burnt or fails to ignite.
The critical chemical kinetic processes in RCCI and SCCI combustion can further be identified by evaluating the explosive index (EI) and participation index (PI) of local mixture. EIand PI are defined as [59, 62]:
EI= |ae⊗bTe|
sum(|be⊗bTe|), (3.2)
PI= |be·S⊗R|
sum(|(be·S)⊗R|), (3.3)
where S and R represent the stoichiometric coefficient matrix and the vector of the net rates for reactions, respectively. The symbol⊗represents the element-wise multiplication of two vectors. Since EI and PI indicate the normalized contribution of each variable and reaction to the CEM, respectively, and as such, controlling species and reactions for RCCI/SCCI combustion can be elucidated by evaluating EI and PI values. Since the mass fractions of quasi-steady state species in the reduced chemistry are functions of the other species, the 171-species skeletal mechanism for PRF oxidation [44] is used to analytically evaluateJω, ae, and be.